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Finite Improbability Calculator

The Finite Improbability Calculator is a collection of routines
to permit exploration of very small probabilities. Many
antievolutionary arguments are based upon an argument from
improbability: some phenomenon is so improbable that it must
be due to an intelligent agent.

Notes on calculations

Factorial: The point here is to permit calculation of
factorial(n) where n can be a large number, say the number of proteins
which an organism codes for. However, even a "double"
floating-point number overflows at 1.7e308. So factorials are
calculated here using a logarithmic representation. The Stirling
approximation is used for very large n, and a logarithmic version of
the classical iterative method is used for smaller n. Stirling's
approximation is taken as

Specified Anti-Information is an application of the "universal
distribution" of Kirchherr et alia 1997, expounded in Elsberry and
Shallit 2003. SAI is a framework intended as an alternative to
Dembski's "design inference". The SAI of a bit string is defined
as

SAI = max(0,|y| - C(y))

where |y| is the length of the bit string of interest and
C(y) is the Kolmogorov complexity of y. Since C(y) is
uncomputable, mostly we should speak of Known Specified
Anti-Information, which is just the maximum SAI that can
be established by application of known compression
techniques.

SAI is defined for bit strings, but often we deal with
strings based on a symbol set with cardinality > 2. It is
straightforward to determine the length of a bit string
needed to represent such a string, though, using the "change of
base" function presented earlier. The second part of the SAI
section permits SAI to be calculated for such strings.

Something to note here is the apparent difference in
ease of application of SAI with the various measures
introduced by Dembski.

The discussion on page 301 implies that functional proteins may
themselves be considered "discrete combinatorial objects" to
which this formula would apply. With a little exploration, then,
one can verify that any functional protein of length 1153 or greater
has an origination probability smaller than Dembski's "universal
small probability".

plocal calculation (as per NFL p.293):

plocal = (units in system * substitutions / total different
units) (units in system * copies)

There is a discrepancy between the result which Dembski reports
for his
example calculation of an M/N ratio on p.297 and what the Finite
Improbability
Calculator reports. Plug in symbols=30, length=1000,
identity=0.2 and the result comes out as 5.555117e-223, whereas
Dembski
reports 10^-288, or a factor of 10^-65 off. Jeff Shallit noted
this
error in Dembski's text some time back.

That error might be measured in a unit called "dembskis" that scaled things in terms of orders of magnitude came up in discussion of errors in an essay by Marks and Dembski. The reference unit of error for the measure is taken from the case mentioned above in the M/N ratio calculation note, where Dembski had an error of about 65 orders of magnitude. "Dave W." formalized the notion with an equation, and W. Kevin Vicklund suggested using a rounded-off value of 150 as the constant in the denominator, based upon Dembski's figure of 10^150 as a universal small probability. Thus, the final form of quantifying error in dembskis (Reed Cartwright proposed the symbol Δ) is

Δ = | ln(erroneous measure) - ln(correct measure) | / 150

There is not yet a consensus on what to term the unit, but two proposals being considered are "Dmb" and "duns".

Hazen Functional Complexity

The calculation is made per the 2007 PNAS paper by Hazen et al.. Given a number of possible configurations, N, and a (smaller) number of functionally equivalent configurations, M(Ex), one obtains the functional complexity metric, I(Ex) as:

The Finite Improbability Calculator was first coded in spring of 2002, following publication of William Dembski's book, "No Free Lunch". The original utilized a Perl CGI script. The FIC was ported to a PHP instantiation in January, 2004, with routines added for calculating Specified Anti-Information. The FIC then was altered to work within a Drupal page using the "PHP code" option.

The name of this page was inspired by "The Hitchhiker's Guide to the Galaxy" by the late great Douglas Adams.

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Antievolutionists Say the Darndest Things

Antievolutionists often express outrage over alleged incivility from those who oppose their efforts to evade the establishment clause of the First Amendment. But they have no difficulty in dishing out the abuse themselves. Here is a sample from the Invidious Comparisons thread that documents egregious behavior on the part of the religious antievolution advocates.

IDC advocate Phillip E. Johnson:

Gould’s uncomfortable situation reminds me of the self-created predicament of Mikhail Gorbachev in the last years of the Soviet Empire. Gorbachev recognized that something had gone wrong with the Communist system, but thought that the system itself could be preserved if it was reformed. His democratic friends warned him that the Marxist fundamentalists would inevitably turn against him, but he was unwilling to endanger his position in the ruling elite by following his own logic to its necessary conclusion. Gould, like Gorbachev, deserves immense credit for bringing glasnost to a closed society of dogmatists. And, like Gorbachev, he lives on as a sad reminder of what happens to those who lack the nerve to make a clean break with a dying theory.